TSTP Solution File: SYO171^5 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SYO171^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 17:32:31 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 36 unt; 3 typ; 0 def)
% Number of atoms : 296 ( 53 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 746 ( 147 ~; 120 |; 24 &; 455 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 146 ( 0 ^ 146 !; 0 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i > $o ).
thf(1,conjecture,
~ ( ! [A: $i] :
( ( g @ A @ a )
| ( g @ ( f @ A ) @ A ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ A @ ( f @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ ( f @ B ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ B @ ( f @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ~ ( g @ B @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSYN031_1) ).
thf(2,negated_conjecture,
( ( ~ ( ! [A: $i] :
( ( g @ A @ a )
| ( g @ ( f @ A ) @ A ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ A @ ( f @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ ( f @ B ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ B @ ( f @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ~ ( g @ B @ a ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ ( ! [A: $i] :
( ( g @ A @ a )
| ( g @ ( f @ A ) @ A ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ A @ ( f @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ ( f @ B ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ B @ ( f @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ~ ( g @ B @ a ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i] :
( ( g @ A @ a )
| ( g @ ( f @ A ) @ A ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ A @ ( f @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ ( f @ B ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ B @ ( f @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ~ ( g @ B @ a ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ~ ( g @ B @ a ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ B @ ( f @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ ( f @ B ) @ B ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ ( f @ A ) @ A ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ A @ ( f @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(6,plain,
( ( ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ~ ( g @ B @ a ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ B @ ( f @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( g @ A @ B )
| ( g @ ( f @ B ) @ B ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ ( f @ A ) @ A ) )
& ! [A: $i] :
( ( g @ A @ a )
| ( g @ A @ ( f @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ~ ( g @ SX1 @ a ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ~ ( g @ SX1 @ a ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[7]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ~ ( g @ SX1 @ a ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(10,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ~ ( g @ SX1 @ a ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[9]) ).
thf(12,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(13,plain,
! [SV1: $i] :
( ( ! [SY8: $i] :
( ~ ( g @ SV1 @ SY8 )
| ~ ( g @ SY8 @ a ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ~ ( g @ SV1 @ SV2 )
| ~ ( g @ SV2 @ a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV2: $i,SV1: $i] :
( ( ( ~ ( g @ SV1 @ SV2 ) )
= $true )
| ( ( ~ ( g @ SV2 @ a ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ SX1 @ ( f @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(21,plain,
! [SV2: $i,SV1: $i] :
( ( ( g @ SV1 @ SV2 )
= $false )
| ( ( ~ ( g @ SV2 @ a ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY9: $i] :
( ~ ( g @ SV3 @ SY9 )
| ( g @ SY9 @ ( f @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i,SV2: $i] :
( ( ( g @ SV2 @ a )
= $false )
| ( ( g @ SV1 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
! [SV4: $i,SV3: $i] :
( ( ~ ( g @ SV3 @ SV4 )
| ( g @ SV4 @ ( f @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: $i,SV3: $i] :
( ( ( ~ ( g @ SV3 @ SV4 ) )
= $true )
| ( ( g @ SV4 @ ( f @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( g @ SX0 @ SX1 )
| ( g @ ( f @ SX1 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
! [SV4: $i,SV3: $i] :
( ( ( g @ SV3 @ SV4 )
= $false )
| ( ( g @ SV4 @ ( f @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: $i] :
( ( ! [SY10: $i] :
( ~ ( g @ SV5 @ SY10 )
| ( g @ ( f @ SY10 ) @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) )
| ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV6: $i,SV5: $i] :
( ( ~ ( g @ SV5 @ SV6 )
| ( g @ ( f @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( ~ ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: $i,SV5: $i] :
( ( ( ~ ( g @ SV5 @ SV6 ) )
= $true )
| ( ( g @ ( f @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ ( f @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [SX0: $i] :
( ( g @ SX0 @ a )
| ( g @ SX0 @ ( f @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i,SV5: $i] :
( ( ( g @ SV5 @ SV6 )
= $false )
| ( ( g @ ( f @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: $i] :
( ( ( g @ SV7 @ a )
| ( g @ ( f @ SV7 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV8: $i] :
( ( ( g @ SV8 @ a )
| ( g @ SV8 @ ( f @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV7: $i] :
( ( ( g @ SV7 @ a )
= $true )
| ( ( g @ ( f @ SV7 ) @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(44,plain,
! [SV8: $i] :
( ( ( g @ SV8 @ a )
= $true )
| ( ( g @ SV8 @ ( f @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,44,43,40,31]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO171^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 08:15:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38 %**** Beginning of derivation protocol ****
% 0.13/0.38 % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38 %**** End of derivation protocol ****
% 0.13/0.38 %**** no. of clauses in derivation: 46 ****
% 0.13/0.38 %**** clause counter: 45 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------